Biochemical network modelling has been mostly developed in terms of
either purely continuous or purely discrete dynamics. However, it
appears that certain processes are more naturally described by models
that feature both continuous evolution and discrete events. In addition,
it is being recognized that many biological processes are intrinsically
uncertain. For instance, stochastic phenomena appear to be instrumental
for certain biochemical processes to induce variability or even to
improve robustness.

In this talk we shall discuss modelling and identification of genetic
networks in a stochastic hybrid framework.

A piecewise deterministic model is introduced where the deterministic
evolution of protein concentration levels is driven by the random
activation and deactivation of gene expression. In turn, gene expression
follows the laws of a finite Markov chain whose transition rates depend
on the current protein concentrations. In our opinion, this modelling
framework provides a tradeoff between accuracy and tractability which is
not offered by more complex models and is well suited for genetic
network analysis and model identification/validation.

Based on this framework, we discuss parameter identification under the
assumption that the genetic interaction pattern is known. We present a
method for the estimation of the unknown model parameters from protein
concentration time profiles.

The procedure performs separate estimation of the dynamics of every gene
in the network and can cope with sparse and noisy measurements. The
computational complexity of the algorithm grows nicely with the size of
the problem, which makes it applicable to fairly large genetic network
models. Results from numerical experiments on simulated data will be
presented to show the estimation performance.